arXiv subjects
Publications and source records attributed to Abderrahman Baza.
In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} ϕ(x+y-z)+ϕ(x+z-y)+ϕ(y+z-x)=ϕ(x-y)+ϕ(x-z)+ϕ(z-y) +ϕ(x)+ϕ(y) +ϕ(z) \end{multline*} in modular space, with or without $Δ_2$-condition, and in $β$-homogeneous Banach space.
In this paper, we investigate some hyperstability results, inspired by the concept of Ulam stability, for the following functional equations: \begin{equation} φ(x+y)+φ(x-y)=2φ(x)+2φ(y) \end{equation} \begin{equation} φ(ax+by) = Aφ(x)+Bφ(y)+C \end{equation} \begin{equation}\label{eqnd} f\left(\sum_{i=1}^{m}x_{i}\right)+\sum_{1\leq i<j\leq m}f\big(x_{i}-x_{j}\big)=m\sum_{i=1}^{m}f(x_{i}) \end{equation} in modular spaces.
In this work, we prove the generalised Hyer Ulam stability of the following functional equation \begin{equation}\label{Eq-1} ϕ(x)+ϕ(y)+ϕ(z)=q ϕ\left(\sqrt[s]{\frac{x^s+y^s+z^s}{q}}\right),\qquad |q| \leq 1 \end{equation} and $s$ is an odd integer such that $s\geq 3$, in modular space, using the direct method, and the fixed point theorem.
Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} ϕ(x+y, z+w)+ϕ(x-y, z-w)-2 ϕ(x, z)-2 ϕ(x, w)=0 \end{equation} in modular space satisfying the Fatou property or $Δ_2$-condition.